Question: Which of the following numbers is a factor of 78? ${6,8,9,11,12}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $78$ by each of our answer choices. $78 \div 6 = 13$ $78 \div 8 = 9\text{ R }6$ $78 \div 9 = 8\text{ R }6$ $78 \div 11 = 7\text{ R }1$ $78 \div 12 = 6\text{ R }6$ The only answer choice that divides into $78$ with no remainder is $6$ $ 13$ $6$ $78$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $6$ are contained within the prime factors of $78$ $78 = 2\times3\times13 6 = 2\times3$ Therefore the only factor of $78$ out of our choices is $6$. We can say that $78$ is divisible by $6$.